arXiv Machine Learning By T. Y. Tsui, Jiatao Gu, Lingjie Liu

The Lattice of Transition Laws

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The paper introduces a framework that unifies diffusion and autoregressive (AR) generative models as paths on a corruption lattice, defining a cost for decoding schedules based on discarded parallel steps. It shows that the minimal number of steps for a zero‑cost schedule is determined by the data’s geometry—specifically, the graph’s treedepth for Markov data—providing a theoretical limit for both token and continuous field models. By estimating pairwise dependencies from pretrained weights, the authors predict the ranking of decoding schedules before execution, and validate these predictions across text, image, and video generation tasks.

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